Commit 9e553a57 authored by ppanchal's avatar ppanchal
Browse files

BEM solver works for single sphere

parent 658fc441
close all; clc; clear;
addpath(genpath("../../../../"));
format long;
global X;
global W;
load('X3','X');
load('W3','W');
% Initializing parameters for the problem
Nvals = 100:50:1700;
sz = size(Nvals,2);
l2errs = zeros(sz,1);
averrs = zeros(sz,1);
linferrs = zeros(sz,1);
Tn_nearest = zeros(sz,1);
Tn_plane = zeros(sz,1);
% Radius of the sphere
Rad = 5;
for ii = 1:sz
N = Nvals(ii)
% Mesh for the geometry
mesh = mshSphere(N,Rad);
% Translate the sphere
%sph_vtcs = mesh_sph.vtx;
%sph_vtcs(:,1) = sph_vtcs(:,1)*0.5;
%mesh_sph.vtx = sph_vtcs;
mesh.vtx = mesh.vtx + ones(size(mesh.vtx,1),1) * [1 0 0];
figure;
plot(mesh);
title('Mesh and normals');
hold on;
% Checking the normal direction for the mesh
ctrs = mesh.ctr;
nrms = mesh.nrm;
quiver3(ctrs(:,1),ctrs(:,2),ctrs(:,3),nrms(:,1),nrms(:,2),nrms(:,3));
scatter3(0,0,0);
%% BEM
% Definition of FEM spaces and integration rule
S1_Gamma = fem(mesh,'P1');
S0_Gamma = fem(mesh,'P0');
order = 3;
Gamma = dom(mesh,order);
% Solving a Direct first kind BVP to get the representation of the state
% V Psi = (0.5*M+K) g_N (Interior problem)
% V Psi = (-0.5*M+K) g_N (Exterior problem)
% Getting the Single Layer matrix V using Gypsilab implementation
Gxy = @(X,Y)femGreenKernel(X,Y,'[1/r]',0); % 0 wave number
V = 1/(4*pi)*integral(Gamma,Gamma,S0_Gamma,Gxy,S0_Gamma);
V = V + 1/(4*pi)*regularize(Gamma,Gamma,S0_Gamma,'[1/r]',S0_Gamma);
% Getting the Double Layer matrix K using Gypsilab implementation
GradG = cell(3,1);
GradG{1} = @(X,Y)femGreenKernel(X,Y,'grady[1/r]1',0);
GradG{2} = @(X,Y)femGreenKernel(X,Y,'grady[1/r]2',0);
GradG{3} = @(X,Y)femGreenKernel(X,Y,'grady[1/r]3',0);
K = 1/(4*pi)*integral(Gamma,Gamma,S0_Gamma,GradG,ntimes(S0_Gamma));
K = K +1/(4*pi)*regularize(Gamma,Gamma,S0_Gamma,'grady[1/r]',ntimes(S0_Gamma));
% Defining the mass matrix M
M = integral(Gamma,S0_Gamma,S0_Gamma);
% Defining the Dirichlet boundary condition
g = @(x) (x(:,1)==x(:,1))*1; % Point charge at origin
figure;
plot(mesh);
hold on;
plot(mesh,g(S0_Gamma.dof));
title('Dirichlet Boundary Condition');
colorbar;
% Constructing the RHS
g_N = integral(Gamma,S0_Gamma,g);
% Exterior problem
Psi = V\((-0.5 * M + K)* (M\g_N));
% Visualizing the Neumann trace
dofs = S0_Gamma.dof;
normals = mesh.nrm;
sPsi = -2*Psi;
figure;
plot(mesh);
hold on;
quiver3(dofs(:,1),dofs(:,2),dofs(:,3),normals(:,1).*sPsi,normals(:,2).*sPsi,normals(:,3).*sPsi);
title('Field on the surface');
%quiver3(dofs(:,1),dofs(:,2),dofs(:,3),normals(:,1),normals(:,2),normals(:,3));
% Visualizing the charge density on the surface of the objects
figure;
plot(mesh);
hold on;
plot(mesh,Psi);
title("Surface charge density");
colorbar;
%% Checking the convergence of the Neumann trace at a point
testpt = [Rad+1 0 0];
dofs = S0_Gamma.dof;
Ndofs = size(dofs,1);
distances = vecnorm((dofs - ones(Ndofs,1) * testpt),2,2);
[min_d,min_ind] = min(distances);
Tn_nearest(ii) = Psi(min_ind)
min_d
dofs(min_ind,:)
%% Using the plane method
elts = mesh.elt;
vtcs = mesh.vtx;
Nelts = size(elts,1);
dist_elts = zeros(Nelts,1);
for i = 1:Nelts
dist_elts(i) = dist_plane(testpt,vtcs(elts(i,1),:),vtcs(elts(i,2),:),vtcs(elts(i,3),:));
end
[mind_plane,minind_plane] = min(dist_elts)
Tn_plane(ii) = Psi(minind_plane)
%% Exact solution
Psi_exact = -1/Rad * (Psi == Psi);
% Visualizing the exactness
figure;
plot(Psi./Psi_exact);
title('Psi/Psi exact');
err_vec = Psi-Psi_exact;
% L2 Error
l2errs(ii) = err_vec' * M * err_vec %norm(err_vec)
averrs(ii) = err_vec' * V * err_vec
linferrs(ii) = max(abs(err_vec))
close all;
end
save('analytic_sol_sph_1.mat',"averrs","l2errs","Tn_plane","Tn_nearest","Nvals","linferrs");
\ No newline at end of file
Nvals = Nvals';
sz = size(Nvals,1);
figure;
loglog(Nvals,averrs);
title('Av errors');
figure;
loglog(Nvals,l2errs);
title('L2 errors');
figure;
loglog(Nvals,linferrs);
title('Linf errors');
% Checking the pt wise convergence of the trace
figure;
loglog(Nvals(1:sz-1),abs(Tn_plane(1:sz-1)-Tn_plane(sz)));
hold on;
loglog(Nvals(1:sz-1),abs(Tn_nearest(1:sz-1)-Tn_nearest(sz)));
legend('Plane','Nearest DOF');
title('Pt convergence');
%%
% Checking the pt wise convergence of the trace
figure;
loglog(Nvals(1:sz-1),abs(Tn_plane(1:sz-1)+1/Rad));
hold on;
loglog(Nvals(1:sz-1),abs(Tn_nearest(1:sz-1)+1/Rad));
legend('Plane','Nearest DOF');
title('Pt convergence');
\ No newline at end of file
......@@ -14,9 +14,11 @@ loglog(Nvals,linferrs);
title('Linf errors');
% Checking the pt wise convergence of the trace
exact_val = -1/4/pi/36;
figure;
loglog(Nvals(1:sz-1),abs(Tn_plane(1:sz-1)-Tn_plane(sz)));
%loglog(Nvals(1:sz-1),abs(Tn_plane(1:sz-1)-Tn_plane(sz)));
loglog(Nvals,abs(Tn_plane-exact_val));
hold on;
loglog(Nvals(1:sz-1),abs(Tn_nearest(1:sz-1)-Tn_nearest(sz)));
loglog(Nvals(1:sz),abs(Tn_nearest-exact_val));
legend('Plane','Nearest DOF');
title('Pt convergence');
\ No newline at end of file
......@@ -11,11 +11,15 @@ A = rand(3,3);
[Q,R] = qr(A);
% Initializing parameters for the problem
N = 100;
Nvals =[];
traces =[];
traces_plane = [];
Nvals = 100:50:1700;
sz = size(Nvals,2);
l2errs = zeros(sz,1);
averrs = zeros(sz,1);
linferrs = zeros(sz,1);
Tn_nearest = zeros(sz,1);
Tn_plane = zeros(sz,1);
% Radius of the sphere
Rad = 5;
......@@ -23,9 +27,9 @@ Rad = 5;
% Radii for the torus
r1 = 5;
r2 = 2;
for N = 100:50:1900
N
Nvals = [Nvals; N];
for ii = 1:sz
N = Nvals(ii)
% Mesh for the geometry
mesh_sph = mshSphere(N,Rad);
mesh_tor = mshTorus(N,r1,r2);
......@@ -112,9 +116,6 @@ Psi = V\((-0.5 * M + K)* (M\g_N));
Psi_tor = Proj_Op_tor * Psi;
Psi_sph = Proj_Op_sph * Psi;
% Solving the adjoint problem to get the adjoint solution
Rho = V\(-0.5 * g_N);
% Visualizing the Neumann trace
dofs = S0_Gamma.dof;
normals = mesh.nrm;
......@@ -140,10 +141,9 @@ dofs = S0_Gamma.dof;
Ndofs = size(dofs,1);
distances = vecnorm((dofs - ones(Ndofs,1) * testpt),2,2);
[min_d,min_ind] = min(distances);
Psi_testpt = Psi(min_ind)
Tn_nearest(ii) = Psi(min_ind)
min_d
dofs(min_ind,:)
traces = [traces; Psi_testpt];
%% Using the plane method
elts = mesh.elt;
......@@ -158,8 +158,7 @@ end
[mind_plane,minind_plane] = min(dist_elts)
Psi_testpt_plane = Psi(minind_plane)
traces_plane = [traces_plane; Psi_testpt_plane];
Tn_plane(ii) = Psi(minind_plane)
%% Exact solution
Psi_exact = -1/4/pi./vecnorm(dofs,2,2).^3 .* (dot(dofs,nrms,2));
Psi_tor_exact = Proj_Op_tor * Psi_exact;
......@@ -181,11 +180,13 @@ title('Psi tor/Psi tor exact');
err_vec = Psi-Psi_exact;
% L2 Error
l2_err = err_vec' * M * err_vec%norm(err_vec)
l2errs(ii) = err_vec' * M * err_vec %norm(err_vec)
av_err = err_vec' * V * err_vec
averrs(ii) = err_vec' * V * err_vec
linf_err = max(abs(err_vec))
linferrs(ii) = max(abs(err_vec))
close all;
end
\ No newline at end of file
end
save('analytic_sol_sph_tor.mat',"averrs","l2errs","Tn_plane","Tn_nearest","Nvals","linferrs");
\ No newline at end of file
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